$\frac{a^2 - ab - bc - c^2}{b^2 - a^2 + 2ac - c^2} = \frac{(a^2 - c^2) - (ab + bc)}{b^2 - (a^2 - 2ac + c^2)} = \frac{(a - c)(a + c) - b(a + c)}{b^2 - (a - c)^2} = \frac{(a + c)(a - c - b)}{(b - (a - c))(b + a - c)} = \frac{(a + c)(a - c - b)}{(b - a + c)(b + a - c)} = \frac{(a + c)(a - c - b)}{-(a - c - b)(b + a - c)} = \frac{a + c}{-(a + b - c)} = \frac{a + c}{c - a - b}$

$\frac{2xy - 3 + 3x - 2y}{9 + 12y + 4y^2} = \frac{(2xy - 2y) - (3 - 3x)}{(3 + 2y)^2} = \frac{2y(x - 1) - 3(1 - x)}{(3 + 2y)^2} = \frac{2y(x - 1) + 3(x - 1)}{(3 + 2y)^2} = \frac{(x - 1)(3 + 2y)}{(3 + 2y)^2} = \frac{x - 1}{2y + 3}$

$\frac{ax^2 - 2x^2 - ay^2 + 2y^2}{ax + ay - 2x - 2y} = \frac{(ax^2 - 2x^2) - (ay^2 - 2y^2)}{(ax + ay) - (2x + 2y)} = \frac{x^2(a - 2) - y^2(a - 2)}{a(x + y) - 2(x + y)} = \frac{(a - 2)(x^2 - y^2)}{(x + y)(a - 2)} = \frac{(x - y)(x + y)}{x +y} = x - y$

$\frac{3xy - 2x - 3y + 2}{x^2 - 2x + 1} = \frac{(3xy - 3y) - (2x - 2)}{(x - 1)^2} = \frac{3y(x - 1) - 2(x - 1)}{(x - 1)^2} = \frac{(x - 1)(3y - 2)}{(x - 1)^2} = \frac{3y - 2}{x - 1}$